That huge drop in tent-camping at Big Bend during the summer is a solid warning. If you do, I highly recommend doing so in the mountains, where it can be 20-40F cooler than the lower altitudes.
I camped at Chisos Basin in July a couple years ago. We were hoping to canoe and camp along the river for a night, but that section of the Rio Grande was mostly dried up at the time. The days were in the 90s and the nights were mid-80s. At lower altitudes, the temps were around 115F during the day.
Regardless, I highly recommend the park overall. It's absolutely breathtaking. We did the Lost Mine trail, which is about 5 miles round trip. The view at the top is just outstanding.